Finite Group Databasebeta

← #7090831

Subgroups — #7090831

Order 512.

1817 conjugacy classes of subgroups.

The subgroup lattice has 1409 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59843C211yesmaximal, characteristic, complemented
2#59421C211yesmaximal, characteristic, complemented
3#32665C211yesmaximal, characteristic, complemented
4#32561C211yesmaximal, characteristic, complemented
5#31994C211yesmaximal, characteristic, complemented
6#31612C211yesmaximal, characteristic, complemented
7#31559C211yesmaximal, characteristic, complemented
8#31308C211yesmaximal, characteristic, complemented
9#31010C211yesmaximal, characteristic, complemented
10#30396C211yesmaximal, characteristic
11#29372C211yesmaximal, characteristic, complemented
12#29369C211yesmaximal, characteristic, complemented
13#29054C211yesmaximal, characteristic, complemented
14#27535C211yesmaximal, characteristic, complemented
15#26975C211yesmaximal, characteristic, complemented
16#26944C211yesmaximal, characteristic, complemented
17#26570C211yesmaximal, characteristic, complemented
18#25164C211yesmaximal, characteristic, complemented
19#25090C211yesmaximal, characteristic, complemented
20#24917C211yesmaximal, characteristic, complemented
21#24910C211yesmaximal, characteristic, complemented
22#24359C211yesmaximal, characteristic, complemented
23#24205C211yesmaximal, characteristic, complemented
24#24205C211yesmaximal, characteristic, complemented
25#24041C211yesmaximal, characteristic, complemented
26#23855C211yesmaximal, characteristic, complemented
27#23683C211yesmaximal, characteristic, complemented
28#22855C211yesmaximal, characteristic, complemented
29#22437C211yesmaximal, characteristic, complemented
30#22395C211yesmaximal, characteristic, complemented
31#22155C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#556C2211yescharacteristic, complemented
34C2×#551—21no—
35C2×D4×Q8C2211yescharacteristic
36C2×#483C2211yescharacteristic, complemented
37C2×#466C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#448C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×#440C2211yescharacteristic
48C2×#440C2211yescharacteristic
49C22×#103C2211yescharacteristic, complemented
50#2728—21no—
51#2702—21no—
52#2702—21no—
53#2697—21no—
54#2609—21no—
55#2582C2211yescharacteristic, complemented
56#2560—21no—
57#2560—21no—
58#2538C2211yescharacteristic
59#2538C2211yescharacteristic
60#2537C2211yescharacteristic
61#2496C2211yescharacteristic
62#2496C2211yescharacteristic
63#2492—21no—
64#2486C2211yescharacteristic
65#2480—21no—
66#2480—21no—
67#2457—21no—
68#2457—21no—
69#2439—21no—
70#2436C2211yescharacteristic
71#2436C2211yescharacteristic, complemented
72#2427—21no—
73#2426C2211yescharacteristic
74#2426C2211yescharacteristic, complemented
75#2422C2211yescharacteristic
76#2422C2211yescharacteristic
77#2421C2211yescharacteristic
78#2421C2211yescharacteristic, complemented
79#2408C2211yescharacteristic
80#2363—21no—
81#2361C2211yescharacteristic
82#2361C2211yescharacteristic
83Q8×C22⋊C4C2211yescharacteristic
84Q8×C22⋊C4C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87C4×C4⋊Q8C2211yescharacteristic, complemented
88C4×#124C2211yescharacteristic
89C4×#124C2211yescharacteristic, complemented
90#2293C2211yescharacteristic
91#2293C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2095C2211yescharacteristic, complemented
96#2093C2211yescharacteristic
97#2092C2211yescharacteristic
98#2088C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2068C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2042C2211yescharacteristic, complemented
116#2042C2211yescharacteristic, complemented
117#2042C2211yescharacteristic, complemented
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic, complemented
124#2013C2211yescharacteristic
125#2013C2211yescharacteristic
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#1999C2211yescharacteristic
132#1985C2211yescharacteristic, complemented
133#1985C2211yescharacteristic, complemented
134#1983C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1972C2211yescharacteristic
138#1959C2211yescharacteristic, complemented
139#1959C2211yescharacteristic, complemented
140#1949C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1926C2211yescharacteristic, complemented
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic, complemented
153#1924C2211yescharacteristic, complemented
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic, complemented
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1874C2211yescharacteristic, complemented
173#1869C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1852C2211yescharacteristic, complemented
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1839C2211yescharacteristic, complemented
189#1808C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198#1767C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201#1752C2211yescharacteristic
202#1752C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16—24no—
207C22×SD16—42no—
208C22×SD16—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#556—42no—
220#556—42no—
221#551—48no—
222D4×Q8—42no—
223D4×Q8—42no—
224C2×C4⋊Q8—21no—
225C2×C4⋊Q8C2311yescharacteristic
226C2×#126—21no—
227C2×#126—21no—
228C2×#126—21no—
229C2×#126—21no—
230C2×#124D411yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×#123—21no—
236C2×#123—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8—21no—
241C2×C22⋊Q8—21no—
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×#121—21no—
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4—21no—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×#117—21no—
266C2×#117—21no—
267C2×#117—21no—
268C22×C4⋊C4C2311yescharacteristic
269C22×C22⋊C4—21no—
270C22×C22⋊C4—21no—
271#483—42no—
272#466—42no—
273#463—24no—
274#463—42no—
275#463—42no—
276#450—42no—
277#448—24no—
278#448—42no—
279#447—42no—
280#440—42no—
281#440—42no—
282#440—42no—
283#440—42no—
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×#103—42no—
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×#97C2311yescharacteristic
339#400—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#393—21no—
367#393—21no—
368#393—21no—
369#393—21no—
370#392—21no—
371#391—21no—
372#391—21no—
373#391—21no—
374#391—21no—
375#391—21no—
376#391D411yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#390—21no—
383#390—21no—
384#390D411yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#389—21no—
393#389—21no—
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388D411yescharacteristic
416#388D411yescharacteristic
417#388D411yescharacteristic
418#388D411yescharacteristic
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#382D411yescharacteristic
441#382C2311yescharacteristic
442#381—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455#379—21no—
456#379—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C43C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500C25—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8C2×D411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4C2×D411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2411yescharacteristic
543C23×C4C2411yescharacteristic
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—416no—
562C2×SD16#4114yes—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8—41no—
569C22×C8—22no—
570C22×C8—41no—
571C22×C8—41no—
572C22×C8—41no—
573C22×C8—41no—
574C22×C8—41no—
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C4⋊Q8—22no—
584C4⋊Q8—22no—
585C4⋊Q8—44no—
586#126—44no—
587#126—44no—
588#126—44no—
589#126—44no—
590#124—24no—
591#124—22no—
592#124—22no—
593#124—22no—
594#124—41no—
595#124—41no—
596#124—41no—
597#123—44no—
598#123—44no—
599#123—44no—
600C22⋊Q8—22no—
601C22⋊Q8—22no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—44no—
605C22⋊Q8—44no—
606C22⋊Q8—44no—
607C22⋊Q8—44no—
608C22⋊Q8—44no—
609#121—22no—
610#121—22no—
611#121—41no—
612#121—41no—
613#121—44no—
614#121—41no—
615#121—41no—
616#121—41no—
617#121—41no—
618#120—44no—
619C4×Q8—22no—
620C4×Q8—22no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×Q8—41no—
631C4×D4—22no—
632C4×D4—22no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—44no—
644C4×D4—44no—
645C4×D4—44no—
646#117—44no—
647#117—44no—
648#117—44no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—41no—
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—44no—
727C2×C22⋊C4—44no—
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42—21no—
743C2×C42—21no—
744C2×C42—21no—
745C2×C42C2×D411yescharacteristic
746C2×C42C2×D411yescharacteristic
747C2×C42C2×D411yescharacteristic
748C2×C42C2×D411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754#107—41no—
755#107—41no—
756#107—41no—
757#107—41no—
758#107—41no—
759#107—41no—
760#106—41no—
761#106—41no—
762C4⋊C8—22no—
763C4⋊C8—41no—
764C4⋊C8—41no—
765C4⋊C8—41no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—22no—
770#103—22no—
771#103—22no—
772#103—22no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#103—41no—
782#103—41no—
783#103—41no—
784#102—22no—
785#102—22no—
786#102—22no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797#102—41no—
798C22⋊C8—22no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804#97—41no—
805#97—41no—
806#97—41no—
807#97—41no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841#95C2×D411yescharacteristic
842#95C2×D411yescharacteristic
843#95C2×D411yescharacteristic
844C24—21no—
845C24—21no—
846C24—21no—
847C24—42no—
848C24—42no—
849C24—42no—
850C24—81no—
851C24—81no—
852C24—81no—
853C24—81no—
854C24C22×D411yescharacteristic
855C24C22×D411yescharacteristic
856C2×Q8—22no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—41no—
873C2×Q8—41no—
874C2×Q8—42no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—42no—
878C2×Q8—44no—
879C2×Q8—44no—
880C2×Q8—81no—
881C2×Q8—81no—
882C2×Q8—82no—
883C2×Q8—82no—
884C2×Q8—82no—
885C2×Q8—82no—
886C2×Q8—82no—
887C2×Q8—82no—
888C2×Q8C2×#4112yes—
889C2×Q8H(5,𝔽2)12yes—
890C2×Q8H(5,𝔽2)12yes—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—41no—
908C2×D4—41no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—44no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—42no—
917C2×D4—42no—
918C2×D4—81no—
919C2×D4—82no—
920C2×D4—82no—
921C2×D4—82no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4AGL(1,ℤ/8)14yes—
929C2×D4C2×#4112yes—
930C2×D4H(5,𝔽2)12yes—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C2511yescharacteristic
993SD16—28no—
994SD16—44no—
995SD16—44no—
996SD16—44no—
997SD16—44no—
998SD16—44no—
999D8—82no—
1000D8—82no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—44no—
1025C2×C8—82no—
1026C2×C8C2×#4112yes—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—41no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—41no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C22⋊C4—22no—
1076C22⋊C4—22no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C42—22no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—41no—
1134C42—41no—
1135C42—41no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—42no—
1141C42—81no—
1142C42—81no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—22no—
1156C23—22no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—84no—
1177C23—84no—
1178C23—84no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23—162no—
1183C23C2×AGL(1,ℤ/8)12yes—
1184C23C2×AGL(1,ℤ/8)12yes—
1185C23C23×D411yescharacteristic
1186Q8—22no—
1187Q8—22no—
1188Q8—22no—
1189Q8—22no—
1190Q8—22no—
1191Q8—22no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—82no—
1199Q8—84no—
1200Q8—84no—
1201D4—22no—
1202D4—22no—
1203D4—22no—
1204D4—22no—
1205D4—44no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—84no—
1215D4—84no—
1216D4—84no—
1217D4—162no—
1218D4—162no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—84no—
1302C2×C4—84no—
1303C2×C4—84no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—162no—
1307C2×C4—162no—
1308C2×C4—162no—
1309C2×C4C2×AGL(1,ℤ/8)12yes—
1310C2×C4C22×#4111yescharacteristic
1311C2×C4C2×H(5,𝔽2)11yescharacteristic
1312C2×C4C2×H(5,𝔽2)11yescharacteristic
1313C2×C4C2×H(5,𝔽2)11yescharacteristic
1314C2×C4#58511yescharacteristic
1315C2×C4#58511yescharacteristic
1316C8—22no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8—41no—
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—42no—
1339C22—42no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—168no—
1360C22D4×#4111yescharacteristic
1361C22#348411yescharacteristic
1362C22#348811yescharacteristic
1363C22C22×AGL(1,ℤ/8)11yescharacteristic
1364C22#358411yescharacteristic
1365C22#358611yescharacteristic
1366C22#358611yescharacteristic
1367C4—22no—
1368C4—41no—
1369C4—41no—
1370C4—41no—
1371C4—41no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4#349011yescharacteristic
1393C4#351311yescharacteristic
1394C4#353411yescharacteristic
1395C4#356011yescharacteristic
1396C2—42no—
1397C2—42no—
1398C2—82no—
1399C2—82no—
1400C2—161no—
1401C2#4423111yescharacteristic
1402C2#6145211yescharacteristic
1403C2#6152811yescharacteristic
1404C2#6157211yescharacteristic
1405C2#6168111yescharacteristic
1406C2#6198911yescharacteristic
1407C2#6208011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30396C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59843C2semidirect
2. #59421C2semidirect
3. #32665C2semidirect
4. #32561C2semidirect
5. #31994C2semidirect
6. #31612C2semidirect
7. #31559C2semidirect
8. #31308C2semidirect
9. #31010C2semidirect
11. #29372C2semidirect
12. #29369C2semidirect
13. #29054C2semidirect
14. #27535C2semidirect
15. #26975C2semidirect
16. #26944C2semidirect
17. #26570C2semidirect
18. #25164C2semidirect
19. #25090C2semidirect
20. #24917C2semidirect
21. #24910C2semidirect
22. #24359C2semidirect
23. #24205C2semidirect
24. #24205C2semidirect
25. #24041C2semidirect
26. #23855C2semidirect
27. #23683C2semidirect
28. #22855C2semidirect
29. #22437C2semidirect
30. #22395C2semidirect
31. #22155C2semidirect
33. C2×#556C22semidirect
36. C2×#483C22semidirect
49. C22×#103C22semidirect
55. #2582C22semidirect
71. #2436C22semidirect
74. #2426C22semidirect
78. #2421C22semidirect
84. Q8×C22⋊C4C22semidirect
87. C4×C4⋊Q8C22semidirect
89. C4×#124C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
94. #2099C22semidirect
95. #2095C22semidirect
98. #2088C22semidirect
99. #2083C22semidirect
100. #2083C22semidirect
103. #2075C22semidirect
104. #2072C22semidirect
106. #2068C22semidirect
107. #2068C22semidirect
108. #2068C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
115. #2042C22semidirect
116. #2042C22semidirect
117. #2042C22semidirect
123. #2033C22semidirect
132. #1985C22semidirect
133. #1985C22semidirect
134. #1983C22semidirect
138. #1959C22semidirect
139. #1959C22semidirect
140. #1949C22semidirect
141. #1943C22semidirect
143. #1936C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
146. #1928C22semidirect
147. #1928C22semidirect
148. #1928C22semidirect
149. #1926C22semidirect
152. #1924C22semidirect
153. #1924C22semidirect
157. #1892C22semidirect
172. #1874C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
183. #1862C22semidirect
184. #1862C22semidirect
185. #1852C22semidirect
187. #1850C22semidirect
188. #1839C22semidirect
191. #1803C22semidirect
192. #1803C22semidirect
196. #1787C22semidirect
198. #1767C22semidirect
199. #1763C22semidirect
200. #1763C22semidirect
202. #1752C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#598432
#594212
#326652
#325612
#319942
#316122
#315592
#313082
#310102
#303962
#293722
#293692
#290542
#275352
#269752
#269442
#265702
#251642
#250902
#249172
#249102
#243592
#242052
#240412
#238552
#236832
#228552
#224372
#223952
#221552